2018 Structural Mechanics II

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Academic unit or major
Undergraduate major in Civil and Environmental Engineering
Hirose Sohichi  Wijeyewickrema Anil 
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Course description and aims

This course has three parts. The first part is concerned with the analysis of statically indeterminate structures by means of superposition of analytical solutions of statically determinate structures or energy principle. The second part gives how to determine plastic limit loads at the failure of structures by use of upper bound theorem and lower bound theorem. The last part focuses on element stiffness equations for truss elements and the direct stiffness method.

In this course, following Structural Mechanics I (CVE.A202), statically indeterminate structures are firstly analysed. It is emphasized that member forces of statically indeterminate structures can be determined by using not only equilibrium equations but also compatibility conditions of structural deformation. Next in the limit analysis called as simple plastic analysis, it is explained that plastic limit loads at the structure failure can be easily obtained using upper and lower bound theorems without taking account of details in failure process. In the direct stiffness method, finally, students learn the basics of matrix structural analysis to solve truss problems.

Student learning outcomes

By completing this course, students will be able to:
1. Determine member forces of statically indeterminate structures, including beam, truss, frame and arch.(S.Hirose)
2. Obtain limit loads at the failure of structures.(S.Hirose)
3. Use global stiffness equations to solve truss problems. (Anil C. W.)
4. Use direct stiffness method to solve truss problems. (Anil C. W.)


statically indeterminate structure, equilibrium equation, compatibility condition, energy principle, limit analysis, upper and lower bound theorems, plastic limit load (S. Hirose)
direct stiffness method, global stiffness equations, truss element stiffness equations (Anil C. W.)

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Part of each class is devoted to fundamentals and the rest to applications. To allow students to get a good understanding of the course contents and practical applications, problems related to the contents of this course are given in homework assignments. Solutions to homework assignments are reviewed in the class.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Analysis of statically indeterminate structures by use of superposition method (S. Hirose) Explain analysis of statically indeterminate structures by use of superposition method, and solve related problems.
Class 2 Analysis of statically indeterminate trusses (S. Hirose) Solve statically indeterminate truss problems.
Class 3 Analysis of statically indeterminate beams, frame and arch structures (S. Hirose) Solve statically indeterminate problems of beams, frame and arch structures.
Class 4 Theory of limit analysis (S. Hirose) Explain theory of limit analysis
Class 5 Application of limit analysis (S. Hirose) Determine limit loads at failure of structures using limit analysis.
Class 6 Element stiffness equations for a truss element (Anil C. W.) Review sections 2.4-2.6 of textbook.
Class 7 Global Analysis Equations – Direct Stiffness Method (Anil C. W.) Review sections 3.1-3.2 of textbook.
Class 8 Examples of Global Analysis Equations – Direct Stiffness (Anil C. W.) Review sections 3.1-3.2 of textbook.


None required. (S. Hirose)
McGuire, W., Gallagher, R. H. and Ziemian, 2000, Matrix Structural Analysis, 2nd edition, John Wiley, New York, USA. (Anil C. W.)

Reference books, course materials, etc.

Lecture materials will be uploaded on OCW-i. (S. Hirose)
Structural Mechanics II,Masaru Matomoto et. al.,Maruzen, JAN:9784621046401 (S. Hirose)

Class notes are available in the Instructor’s HP. (Anil C. W.)
Kassimali, A., 2012, Matrix Analysis of Structures, 2nd edition, Cengage Learning, Connecticut, USA. (Anil C. W.)

Assessment criteria and methods

Final exam 45%, assignment 15% (S. Hirose)

Final exam 30%, exercise problems 10%. (Anil C. W.)
Students' knowledge of structural analysis and their ability to apply them to problems will be assessed.

Related courses

  • CVE.A202 : Structural Mechanics I
  • CVE.A311 : Matrix Methods of Structural Analysis

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Student must have successfully completed Structural Mechanics I (CVE.A202) or have equivalent knowledge.

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